Revisiting the $P$-wave charmonium radiative decays $h_c\to \gamma {\eta }^{(\prime )}$ with relativistic corrections

Abstract

The $P$-wave charmonium decays $h_c\to \gamma {\eta }^{(\prime )}$ are revisited by taking into account relativistic corrections. The decay amplitudes are derived in the Bethe-Salpeter formalism, in which the involved one-loop integrals are evaluated analytically. Intriguingly, from both the quark-antiquark content and the gluonic content of ${\eta }^{(\prime )}$, the relativistic corrections make significant contributions to the decay rates of $h_c\to \gamma {\eta }^{(\prime )}$. By comparison with the leading-order contributions from the quark-antiquark content (one-loop level), the ones from the gluonic content (tree level) are also important, which is compatible with the conclusion obtained without relativistic corrections. Usually, for $\eta$ production processes, the predicted branching ratios are sensitive to the angle of $\eta -{\eta }^{\prime }$ mixing. As an illustration, using the Feldmann-Kroll-Stech result about the mixing angle $\varphi =39.3^{\circ }\pm 1.0^{\circ }$ as input, we find that the predicted ratio $R_{h_c}=\mathcal{B}(h_c\to \gamma \eta )/\mathcal{B}(h_c\to \gamma {\eta }^{\prime })$ is much smaller than the experiment measurement. While, with $\varphi =33.5^{\circ }\pm 0.9^{\circ }$ extracted from the asymptotic limit of the ${\gamma }^{\ast }\gamma -{\eta }^{\prime }$ transition form factor, we obtain $R_{h_c}=30.3\%$ in consistent with $R_{h_c}^{exp}=(30.7\pm 11.3\pm 8.7)\%$. As a cross-check, the mixing angle $\varphi =33.8^{\circ }\pm 2.5^{\circ }$ is extracted by employing the ratio $R_{h_c}$, and a brief discussion on the difference in the determinations of $\varphi$ is given.

arXiv comment34 pages, 4 figures and 7 tables

References in corpus (68)

• Rigorous QCD Analysis of Inclusive Annihilation and Production of Heavy Quarkonium
• Mixing and Decay Constants of Pseudoscalar Mesons
• Package-X: A Mathematica package for the analytic calculation of one-loop integrals
• Charmonium
• Quark structure of pseudoscalar mesons
• Higher Charmonia and X,Y,Z states with Screened Potential
• Mixing and Decay Constants of Pseudoscalar Mesons: The Sequel
• Package-X 2.0: A Mathematica package for the analytic calculation of one-loop integrals
• On the 1/N expansion in chiral perturbation theory
• Rigorous QCD Predictions for Decays of P-Wave Quarkonia
• Phenomenological Evidence for the Gluon Content of $\eta$ and ${\eta }^{\prime }$
• On the gluon content of the eta and eta' mesons
• The two-gluon components of the eta and eta' mesons to leading-twist accuracy
• A global fit to determine the pseudoscalar mixing angle and the gluonium content of the eta' meson
• Measurement of the eta and etaprime transition form factors at q^2=112 GeV^2
• Bottomonium Spectrum with Screened Potential
• B->eta(') Form Factors in QCD
• The ${\eta }^{\prime }$ transition form factor from space- and time-like experimental data
• ηand η' transition form factors from rational approximants
• Transition form factors ${\gamma }^{\ast }\gamma \to \eta$ and ${\gamma }^{\ast }\gamma \to {\eta }^{\prime }$ in QCD
• The eta transition form factor from space- and time-like experimental data
• Revisiting Charmless Two-Body B Decays involving ${\eta }^{\prime }$ and $\eta$
• Analysis of the instantaneous Bethe-Salpeter equation for \(q\bar{q}\)-bound-states
• Flavor-singlet meson decay constants from $N_f=2+1+1$ twisted mass lattice QCD
• A study of the eta and eta' mesons with improved staggered fermions
• Charmonium decays to gamma pi0, gamma eta, and gamma eta'
• Eta-eta' masses and mixing: a large N_c reappraisal
• Pseudoscalar decay constants at large N_c
• J/psi->VP decays and the quark and gluon content of the eta and eta'
• The ${\eta }^{\prime }{g}^{\ast }{g}^{\ast }$ vertex with arbitrary gluon virtualities in the perturbative QCD hard scattering approach
• Measurement of the Matrix Element for the Decay ${\eta }^{\prime }\to \eta {\pi }^{+}{\pi }^{-}$
• Evidence for psi' decays into gamma pi^0 and gamma eta
• Spectroscopy of ground and excited states of pseudoscalar and vector charmonium and bottomonium
• ${\eta }^{\prime }-g^{\ast }-g$ Transition Form Factor with Gluon Content Contribution Tested
• Corrections For Two Photon Decays of chi_{c0} and chi_{c2} and Color Octet Contributions
• Electromagnetic Annihilation Rates of ${\chi }_{c0}$ and ${\chi }_{c2}$ with Both Relativistic and QCD Radiative Corrections
• Unified study of $J/\psi \to PV$, $P{\gamma }^{(\ast )}$ and light hadron radiative processes
• Measurement of η meson production in γγ interactions and Γ(η-->γγ) with the KLOE detector
• Pseuduscalar Heavy Quarkonium Decays With Both Relativistic and QCD Radiative Corrections
• ${\pi }^0$-$\eta$-${\eta }^{\prime }$ mixing from $V\to P\gamma$ and $P\to V\gamma$ decays
• Covariant spectator theory of quark-antiquark bound states: Mass spectra and vertex functions of heavy and heavy-light mesons
• Reexamining radiative decays of $1^{--}$ quarkonium into ${\eta }^{\prime }$ and $\eta$
• Relevance of various Dirac covariants in hadronic Bethe-Salpeter wave functions in electromagnetic decays of ground state vector mesons
• Arranging Dirac covariants in hadronic Bethe-Salpeter wave functions for pseudoscalar meson decays
• The ${\eta }^{\prime }{g}^{\ast }{g}^{(\ast )}$ Vertex Including the ${\eta }^{\prime }$-Meson Mass
• Bethe-Salpeter study of radially excited vector quarkonia
• Analytic approach to calculations of mass spectra and decay constants of heavy-light quarkonia in the framework of Bethe-Salpeter equation
• Revisiting the OZI-forbidden Radiative Decays of Orthoquarkonia
• Observation of $h_c$ radiative decay $h_c\to \gamma {\eta }^{\prime }$ and evidence for $h_c\to \gamma \eta$
• An approach to calculation of mass spectra and two-photon decays of $c\overline{c}$ mesons in the framework of Bethe-Salpeter Equation
• Understanding the radiative decays of vector charmonia to light pseudoscalar mesons
• Measurement of the branching fractions for $J/\psi \to \gamma {\pi }^0$, $\gamma \eta$ and $\gamma {\eta }^{\prime }$
• Exclusive Radiative Z-Boson Decays to Mesons with Flavor-Singlet Components
• Colour Octet Contribution in Exclusive P-Wave Charmonium Decay into Proton-Antiproton
• Ultimate survival in anomalous psi(2S) decays
• Gluonic and leptonic decays of heavy quarkonia and the determination of ${\alpha }_s(m_c)$ and ${\alpha }_s(m_b)$
• Revisiting the radiative decays $J/\psi \to \gamma {\eta }^{(\prime )}$ in perturbative QCD
• Cross section for double charmonium production in electron-positron annihilation at energy $\sqrt{s}$= 10.6 GeV
• Measurement of the eta'-meson mass using J/psi--> gamma eta'
• Rigorous QCD Predictions for Decays of P-Wave Quarkonia
• Scrutinizing the eta-eta' mixing, masses and pseudoscalar decay constants in the framework of U(3) chiral effective field theory
• Measurement of branching fractions for $\psi (3686)\to \gamma {\eta }^{\prime },\gamma \eta$ and $\gamma {\pi }^0$
• Radiative decays of $h_c$ to the light mesons ${\eta }^{(\prime )}$: A perturbative QCD calculation
• Exclusive charmonium decays
• Study on the radiative decays of $h_c$ via intermediate meson loops model
• Colour octet contribution to exclusive P-wave charmonium decay into nucleon-antinucleon
• Color Octet Contribution in Exclusive P-Wave Charmonium Decay
• Radiative $h_{c/b}$ decays to $\eta$ or ${\eta }^{\prime }$

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• $E1$ and M1 radiative transitions involving heavy-light axial, pseudoscalar and vector quarkonia in the framework of Bethe-Salpeter equation
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• Improved measurement of the branching fraction of $h_c\to \gamma {\eta }^{\prime }/\eta$ and search for $h_c\to \gamma {\pi }^0$
• QCD analysis of the $P$-wave charmonium electromagnetic Dalitz decays $h_c\to {\eta }^{(\prime )}{\ell }^{+}{\ell }^{-}$
• Heavy quarkonium decay $V\to ggg$ with both relativistic and QCD radiative corrections